## Subject Block Trial SpeakerPhoto
## Min. : 1.00 Min. :1.000 Min. : 1.00 Length:7280
## 1st Qu.:12.00 1st Qu.:1.000 1st Qu.:20.75 Class :character
## Median :24.00 Median :1.000 Median :40.50 Mode :character
## Mean :23.58 Mean :1.495 Mean :40.50
## 3rd Qu.:35.00 3rd Qu.:2.000 3rd Qu.:60.25
## Max. :46.00 Max. :2.000 Max. :80.00
## Logo Condition TargetButton Button_Response
## Length:7280 Length:7280 Min. :2.0 Min. :0.000
## Class :character Class :character 1st Qu.:2.0 1st Qu.:2.000
## Mode :character Mode :character Median :2.5 Median :2.000
## Mean :2.5 Mean :2.478
## 3rd Qu.:3.0 3rd Qu.:3.000
## Max. :3.0 Max. :3.000
## Accuracy RTs
## Min. :0.0000 Min. : -1639.0
## 1st Qu.:1.0000 1st Qu.: 717.8
## Median :1.0000 Median : 847.0
## Mean :0.9374 Mean : 9544.4
## 3rd Qu.:1.0000 3rd Qu.: 1021.0
## Max. :1.0000 Max. :2100000.0
## Participant Block Trial Group_Membership
## 1 : 160 1:3643 Min. : 1.00 Ingroup :3612
## 2 : 160 2:3575 1st Qu.:21.00 Outgroup:3606
## 4 : 160 Median :41.00
## 5 : 160 Mean :40.53
## 6 : 160 3rd Qu.:61.00
## 7 : 160 Max. :80.00
## (Other):6258
## Condition Accuracy RTs
## matching :3614 Min. :0.0000 Min. : 98.0
## mismatching:3604 1st Qu.:1.0000 1st Qu.: 716.0
## Median :1.0000 Median : 844.0
## Mean :0.9417 Mean : 888.7
## 3rd Qu.:1.0000 3rd Qu.:1015.0
## Max. :1.0000 Max. :2097.0
##
Non sembrano esserci molti errori…
(solitamente skewed)
Le persone sono piu’ veloci a rispondere ad un’associazione corretta che incorreta : –> (RTs) matching<mismatching
Le persone son piu’ veloci a rispondere ad un’associazione in-group che out-group : –> (RTs) in-group
lm(log10(RTs)~GroupMembership*Condition (+ Block))
lmer(log10(RTs)~GroupMembershipxCondition (+ Block)+ (1+GroupMembershipxCondition|Participant))
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## log10(RTs) ~ Condition * Group_Membership + Block + (1 + Condition |
## Participant)
## Data: PMT
## Control: lmerControl(optCtrl = list(optimizer = "bobyqa", maxfun = 1e+09))
##
## REML criterion at convergence: -13833.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.6572 -0.6462 -0.0642 0.6075 3.5722
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Participant (Intercept) 0.0043895 0.06625
## Condition2-1 0.0003631 0.01906 0.23
## Residual 0.0070104 0.08373
## Number of obs: 6657, groups: Participant, 46
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 2.931e+00 9.824e-03 4.499e+01 298.356
## Condition2-1 3.793e-02 3.490e-03 4.367e+01 10.869
## Group_Membership2-1 2.866e-02 2.054e-03 6.567e+03 13.953
## Block2-1 -1.422e-02 2.061e-03 6.567e+03 -6.898
## Condition2-1:Group_Membership2-1 -4.034e-02 4.109e-03 6.564e+03 -9.819
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## Condition2-1 5.29e-14 ***
## Group_Membership2-1 < 2e-16 ***
## Block2-1 5.79e-12 ***
## Condition2-1:Group_Membership2-1 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) Cnd2-1 G_M2-1 Blc2-1
## Conditin2-1 0.183
## Grp_Mmbr2-1 0.001 -0.008
## Block2-1 0.001 -0.002 0.004
## C2-1:G_M2-1 -0.001 0.004 0.014 0.003
| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 2.93 | 0.01 | 44.99 | 298.36 | 0 |
| Condition2-1 | 0.04 | 0.00 | 43.67 | 10.87 | 0 |
| Group_Membership2-1 | 0.03 | 0.00 | 6566.77 | 13.95 | 0 |
| Block2-1 | -0.01 | 0.00 | 6567.31 | -6.90 | 0 |
| Condition2-1:Group_Membership2-1 | -0.04 | 0.00 | 6563.77 | -9.82 | 0 |
| log10(RTs) | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 2.93 | 2.91 – 2.95 | <0.001 |
| Condition2-1 | 0.04 | 0.03 – 0.04 | <0.001 |
| Group_Membership2-1 | 0.03 | 0.02 – 0.03 | <0.001 |
| Block2-1 | -0.01 | -0.02 – -0.01 | <0.001 |
| Condition2-1:Group_Membership2-1 | -0.04 | -0.05 – -0.03 | <0.001 |
| Random Effects | |||
| σ2 | 0.01 | ||
| τ00 Participant | 0.00 | ||
| τ11 Participant.Condition2-1 | 0.00 | ||
| ρ01 Participant | 0.23 | ||
| ICC Participant | 0.39 | ||
| Observations | 6657 | ||
| Marginal R2 / Conditional R2 | 0.060 / 0.426 | ||
L’effetto di Condition e’ maggiore con In-group, pero’..
## $emmeans
## Group_Membership = Ingroup:
## Condition emmean SE df asymp.LCL asymp.UCL
## matching 2.89 0.00976 Inf 2.87 2.91
## mismatching 2.95 0.01039 Inf 2.93 2.97
##
## Group_Membership = Outgroup:
## Condition emmean SE df asymp.LCL asymp.UCL
## matching 2.94 0.00977 Inf 2.92 2.96
## mismatching 2.95 0.01039 Inf 2.93 2.97
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: asymptotic
## Results are given on the log10 (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## Group_Membership = Ingroup:
## contrast estimate SE df z.ratio p.value
## matching - mismatching -0.0581 0.00404 Inf -14.371 <.0001
##
## Group_Membership = Outgroup:
## contrast estimate SE df z.ratio p.value
## matching - mismatching -0.0178 0.00406 Inf -4.379 <.0001
##
## Results are averaged over the levels of: Block
L’effetto di In-group e’ nei maggiormente nei matching trials…
## $emmeans
## Condition = matching:
## Group_Membership emmean SE df asymp.LCL asymp.UCL
## Ingroup 2.89 0.00976 Inf 2.87 2.91
## Outgroup 2.94 0.00977 Inf 2.92 2.96
##
## Condition = mismatching:
## Group_Membership emmean SE df asymp.LCL asymp.UCL
## Ingroup 2.95 0.01039 Inf 2.93 2.97
## Outgroup 2.95 0.01039 Inf 2.93 2.97
##
## Results are averaged over the levels of: Block
## Degrees-of-freedom method: asymptotic
## Results are given on the log10 (not the response) scale.
## Confidence level used: 0.95
##
## $contrasts
## Condition = matching:
## contrast estimate SE df z.ratio p.value
## Ingroup - Outgroup -0.04883 0.00288 Inf -16.929 <.0001
##
## Condition = mismatching:
## contrast estimate SE df z.ratio p.value
## Ingroup - Outgroup -0.00849 0.00293 Inf -2.901 0.0037
##
## Results are averaged over the levels of: Block
I dati hanno supportato le nostre ipotesi. 1. I partecipanti hanno classificato piu’ velocemente un’associazione corretta che incorretta.
E l’interazione dice che c’e’ una differenza tra le condizioni di matching and mismatching per quanto riguarda l’effetto di Group Membership.
Attraverso l’analisi di simple effects (pairwise comparisons), abbiamo visto che i partecipanti erano piu’ veloci con le associazioni in-group ma maggiormente quando un’associazione era corretta.
I mixed-effect models sono importantissimi quando ci sono intra e inter variabilita’ perche’ aiutano a ridurre la possibilita’ di attribuire importanza a cio’ che non ne ha.
Questions?